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Search: id:A073607
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| A073607 |
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Smallest of three consecutive integers divisible by three consecutive primes respectively. |
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+0
8
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| 8, 20, 38, 54, 68, 98, 114, 128, 158, 159, 169, 188, 218, 248, 264, 278, 308, 338, 368, 369, 398, 405, 428, 458, 474, 488, 518, 548, 578, 579, 608, 638, 668, 684, 698, 728, 758, 788, 789, 790, 791, 818, 848, 878, 894, 908, 938, 968, 998, 999, 1028, 1058
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence is infinite as 30k + 8 is a member for all k. What is the longest string of consecutive integers?
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EXAMPLE
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20 is a term as 20,21 and 22 are divisible by 5,7 and 11 respectively. 114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.
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MATHEMATICA
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f[ n_Integer ] := Flatten[ Table[ #1 ] & @@@ FactorInteger[ n ]]; NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[ n + i, {i, 0, 2} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 2 ] ]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 1117} ]
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CROSSREFS
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Cf. A073606, A072555, A073754, A073755, A073756 & A072562.
Sequence in context: A038522 A139570 A004118 this_sequence A086062 A006416 A121307
Adjacent sequences: A073604 A073605 A073606 this_sequence A073608 A073609 A073610
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 04 2002
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 06 2002
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